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  <div class="section" id="data-structures">
<span id="tut-structures"></span><h1>5. Data Structures<a class="headerlink" href="#data-structures" title="Permalink to this headline">¶</a></h1>
<p>This chapter describes some things you&#8217;ve learned about already in more detail,
and adds some new things as well.</p>
<div class="section" id="more-on-lists">
<span id="tut-morelists"></span><h2>5.1. More on Lists<a class="headerlink" href="#more-on-lists" title="Permalink to this headline">¶</a></h2>
<p>The list data type has some more methods.  Here are all of the methods of list
objects:</p>
<dl class="method">
<dt>
<tt class="descclassname">list.</tt><tt class="descname">append</tt><big>(</big><em>x</em><big>)</big></dt>
<dd><p>Add an item to the end of the list; equivalent to <tt class="docutils literal"><span class="pre">a[len(a):]</span> <span class="pre">=</span> <span class="pre">[x]</span></tt>.</p>
</dd></dl>

<dl class="method">
<dt>
<tt class="descclassname">list.</tt><tt class="descname">extend</tt><big>(</big><em>L</em><big>)</big></dt>
<dd><p>Extend the list by appending all the items in the given list; equivalent to
<tt class="docutils literal"><span class="pre">a[len(a):]</span> <span class="pre">=</span> <span class="pre">L</span></tt>.</p>
</dd></dl>

<dl class="method">
<dt>
<tt class="descclassname">list.</tt><tt class="descname">insert</tt><big>(</big><em>i</em>, <em>x</em><big>)</big></dt>
<dd><p>Insert an item at a given position.  The first argument is the index of the
element before which to insert, so <tt class="docutils literal"><span class="pre">a.insert(0,</span> <span class="pre">x)</span></tt> inserts at the front of
the list, and <tt class="docutils literal"><span class="pre">a.insert(len(a),</span> <span class="pre">x)</span></tt> is equivalent to <tt class="docutils literal"><span class="pre">a.append(x)</span></tt>.</p>
</dd></dl>

<dl class="method">
<dt>
<tt class="descclassname">list.</tt><tt class="descname">remove</tt><big>(</big><em>x</em><big>)</big></dt>
<dd><p>Remove the first item from the list whose value is <em>x</em>. It is an error if there
is no such item.</p>
</dd></dl>

<dl class="method">
<dt>
<tt class="descclassname">list.</tt><tt class="descname">pop</tt><big>(</big><span class="optional">[</span><em>i</em><span class="optional">]</span><big>)</big></dt>
<dd><p>Remove the item at the given position in the list, and return it.  If no index
is specified, <tt class="docutils literal"><span class="pre">a.pop()</span></tt> removes and returns the last item in the list.  (The
square brackets around the <em>i</em> in the method signature denote that the parameter
is optional, not that you should type square brackets at that position.  You
will see this notation frequently in the Python Library Reference.)</p>
</dd></dl>

<dl class="method">
<dt>
<tt class="descclassname">list.</tt><tt class="descname">index</tt><big>(</big><em>x</em><big>)</big></dt>
<dd><p>Return the index in the list of the first item whose value is <em>x</em>. It is an
error if there is no such item.</p>
</dd></dl>

<dl class="method">
<dt>
<tt class="descclassname">list.</tt><tt class="descname">count</tt><big>(</big><em>x</em><big>)</big></dt>
<dd><p>Return the number of times <em>x</em> appears in the list.</p>
</dd></dl>

<dl class="method">
<dt>
<tt class="descclassname">list.</tt><tt class="descname">sort</tt><big>(</big><em>cmp=None</em>, <em>key=None</em>, <em>reverse=False</em><big>)</big></dt>
<dd><p>Sort the items of the list in place (the arguments can be used for sort
customization, see <a class="reference internal" href="../library/functions.html#sorted" title="sorted"><tt class="xref py py-func docutils literal"><span class="pre">sorted()</span></tt></a> for their explanation).</p>
</dd></dl>

<dl class="method">
<dt>
<tt class="descclassname">list.</tt><tt class="descname">reverse</tt><big>(</big><big>)</big></dt>
<dd><p>Reverse the elements of the list, in place.</p>
</dd></dl>

<p>An example that uses most of the list methods:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="p">[</span><span class="mf">66.25</span><span class="p">,</span> <span class="mi">333</span><span class="p">,</span> <span class="mi">333</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">1234.5</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="k">print</span> <span class="n">a</span><span class="o">.</span><span class="n">count</span><span class="p">(</span><span class="mi">333</span><span class="p">),</span> <span class="n">a</span><span class="o">.</span><span class="n">count</span><span class="p">(</span><span class="mf">66.25</span><span class="p">),</span> <span class="n">a</span><span class="o">.</span><span class="n">count</span><span class="p">(</span><span class="s">&#39;x&#39;</span><span class="p">)</span>
<span class="go">2 1 0</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span><span class="o">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">333</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span>
<span class="go">[66.25, 333, -1, 333, 1, 1234.5, 333]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="mi">333</span><span class="p">)</span>
<span class="go">1</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="mi">333</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span>
<span class="go">[66.25, -1, 333, 1, 1234.5, 333]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span><span class="o">.</span><span class="n">reverse</span><span class="p">()</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span>
<span class="go">[333, 1234.5, 1, 333, -1, 66.25]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span><span class="o">.</span><span class="n">sort</span><span class="p">()</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span>
<span class="go">[-1, 1, 66.25, 333, 333, 1234.5]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
<span class="go">1234.5</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span>
<span class="go">[-1, 1, 66.25, 333, 333]</span>
</pre></div>
</div>
<p>You might have noticed that methods like <tt class="docutils literal"><span class="pre">insert</span></tt>, <tt class="docutils literal"><span class="pre">remove</span></tt> or <tt class="docutils literal"><span class="pre">sort</span></tt> that
only modify the list have no return value printed &#8211; they return the default
<tt class="xref docutils literal"><span class="pre">None</span></tt>. <a class="footnote-reference" href="#id3" id="id1">[1]</a>  This is a design principle for all mutable data structures in
Python.</p>
<div class="section" id="using-lists-as-stacks">
<span id="tut-lists-as-stacks"></span><h3>5.1.1. Using Lists as Stacks<a class="headerlink" href="#using-lists-as-stacks" title="Permalink to this headline">¶</a></h3>
<p>The list methods make it very easy to use a list as a stack, where the last
element added is the first element retrieved (&#8220;last-in, first-out&#8221;).  To add an
item to the top of the stack, use <tt class="xref py py-meth docutils literal"><span class="pre">append()</span></tt>.  To retrieve an item from the
top of the stack, use <tt class="xref py py-meth docutils literal"><span class="pre">pop()</span></tt> without an explicit index.  For example:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="n">stack</span> <span class="o">=</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">6</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">7</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">stack</span>
<span class="go">[3, 4, 5, 6, 7]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">stack</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
<span class="go">7</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">stack</span>
<span class="go">[3, 4, 5, 6]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">stack</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
<span class="go">6</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">stack</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
<span class="go">5</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">stack</span>
<span class="go">[3, 4]</span>
</pre></div>
</div>
</div>
<div class="section" id="using-lists-as-queues">
<span id="tut-lists-as-queues"></span><h3>5.1.2. Using Lists as Queues<a class="headerlink" href="#using-lists-as-queues" title="Permalink to this headline">¶</a></h3>
<p>It is also possible to use a list as a queue, where the first element added is
the first element retrieved (&#8220;first-in, first-out&#8221;); however, lists are not
efficient for this purpose.  While appends and pops from the end of list are
fast, doing inserts or pops from the beginning of a list is slow (because all
of the other elements have to be shifted by one).</p>
<p>To implement a queue, use <a class="reference internal" href="../library/collections.html#collections.deque" title="collections.deque"><tt class="xref py py-class docutils literal"><span class="pre">collections.deque</span></tt></a> which was designed to
have fast appends and pops from both ends.  For example:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">deque</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">queue</span> <span class="o">=</span> <span class="n">deque</span><span class="p">([</span><span class="s">&quot;Eric&quot;</span><span class="p">,</span> <span class="s">&quot;John&quot;</span><span class="p">,</span> <span class="s">&quot;Michael&quot;</span><span class="p">])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">queue</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s">&quot;Terry&quot;</span><span class="p">)</span>           <span class="c"># Terry arrives</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">queue</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s">&quot;Graham&quot;</span><span class="p">)</span>          <span class="c"># Graham arrives</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">queue</span><span class="o">.</span><span class="n">popleft</span><span class="p">()</span>                 <span class="c"># The first to arrive now leaves</span>
<span class="go">&#39;Eric&#39;</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">queue</span><span class="o">.</span><span class="n">popleft</span><span class="p">()</span>                 <span class="c"># The second to arrive now leaves</span>
<span class="go">&#39;John&#39;</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">queue</span>                           <span class="c"># Remaining queue in order of arrival</span>
<span class="go">deque([&#39;Michael&#39;, &#39;Terry&#39;, &#39;Graham&#39;])</span>
</pre></div>
</div>
</div>
<div class="section" id="functional-programming-tools">
<span id="tut-functional"></span><h3>5.1.3. Functional Programming Tools<a class="headerlink" href="#functional-programming-tools" title="Permalink to this headline">¶</a></h3>
<p>There are three built-in functions that are very useful when used with lists:
<a class="reference internal" href="../library/functions.html#filter" title="filter"><tt class="xref py py-func docutils literal"><span class="pre">filter()</span></tt></a>, <a class="reference internal" href="../library/functions.html#map" title="map"><tt class="xref py py-func docutils literal"><span class="pre">map()</span></tt></a>, and <a class="reference internal" href="../library/functions.html#reduce" title="reduce"><tt class="xref py py-func docutils literal"><span class="pre">reduce()</span></tt></a>.</p>
<p><tt class="docutils literal"><span class="pre">filter(function,</span> <span class="pre">sequence)</span></tt> returns a sequence consisting of those items from
the sequence for which <tt class="docutils literal"><span class="pre">function(item)</span></tt> is true. If <em>sequence</em> is a
<a class="reference internal" href="../library/string.html#module-string" title="string: Common string operations."><tt class="xref py py-class docutils literal"><span class="pre">string</span></tt></a> or <a class="reference internal" href="../library/functions.html#tuple" title="tuple"><tt class="xref py py-class docutils literal"><span class="pre">tuple</span></tt></a>, the result will be of the same type;
otherwise, it is always a <a class="reference internal" href="../library/functions.html#list" title="list"><tt class="xref py py-class docutils literal"><span class="pre">list</span></tt></a>. For example, to compute a sequence of
numbers not divisible by 2 or 3:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="k">def</span> <span class="nf">f</span><span class="p">(</span><span class="n">x</span><span class="p">):</span> <span class="k">return</span> <span class="n">x</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">!=</span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">x</span> <span class="o">%</span> <span class="mi">3</span> <span class="o">!=</span> <span class="mi">0</span>
<span class="gp">...</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">filter</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">25</span><span class="p">))</span>
<span class="go">[5, 7, 11, 13, 17, 19, 23]</span>
</pre></div>
</div>
<p><tt class="docutils literal"><span class="pre">map(function,</span> <span class="pre">sequence)</span></tt> calls <tt class="docutils literal"><span class="pre">function(item)</span></tt> for each of the sequence&#8217;s
items and returns a list of the return values.  For example, to compute some
cubes:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="k">def</span> <span class="nf">cube</span><span class="p">(</span><span class="n">x</span><span class="p">):</span> <span class="k">return</span> <span class="n">x</span><span class="o">*</span><span class="n">x</span><span class="o">*</span><span class="n">x</span>
<span class="gp">...</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">map</span><span class="p">(</span><span class="n">cube</span><span class="p">,</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">11</span><span class="p">))</span>
<span class="go">[1, 8, 27, 64, 125, 216, 343, 512, 729, 1000]</span>
</pre></div>
</div>
<p>More than one sequence may be passed; the function must then have as many
arguments as there are sequences and is called with the corresponding item from
each sequence (or <tt class="xref docutils literal"><span class="pre">None</span></tt> if some sequence is shorter than another).  For
example:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="n">seq</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="mi">8</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="k">def</span> <span class="nf">add</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span> <span class="k">return</span> <span class="n">x</span><span class="o">+</span><span class="n">y</span>
<span class="gp">...</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">map</span><span class="p">(</span><span class="n">add</span><span class="p">,</span> <span class="n">seq</span><span class="p">,</span> <span class="n">seq</span><span class="p">)</span>
<span class="go">[0, 2, 4, 6, 8, 10, 12, 14]</span>
</pre></div>
</div>
<p><tt class="docutils literal"><span class="pre">reduce(function,</span> <span class="pre">sequence)</span></tt> returns a single value constructed by calling the
binary function <em>function</em> on the first two items of the sequence, then on the
result and the next item, and so on.  For example, to compute the sum of the
numbers 1 through 10:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="k">def</span> <span class="nf">add</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">):</span> <span class="k">return</span> <span class="n">x</span><span class="o">+</span><span class="n">y</span>
<span class="gp">...</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">reduce</span><span class="p">(</span><span class="n">add</span><span class="p">,</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">11</span><span class="p">))</span>
<span class="go">55</span>
</pre></div>
</div>
<p>If there&#8217;s only one item in the sequence, its value is returned; if the sequence
is empty, an exception is raised.</p>
<p>A third argument can be passed to indicate the starting value.  In this case the
starting value is returned for an empty sequence, and the function is first
applied to the starting value and the first sequence item, then to the result
and the next item, and so on.  For example,</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="k">def</span> <span class="nf">sum</span><span class="p">(</span><span class="n">seq</span><span class="p">):</span>
<span class="gp">... </span>    <span class="k">def</span> <span class="nf">add</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">):</span> <span class="k">return</span> <span class="n">x</span><span class="o">+</span><span class="n">y</span>
<span class="gp">... </span>    <span class="k">return</span> <span class="nb">reduce</span><span class="p">(</span><span class="n">add</span><span class="p">,</span> <span class="n">seq</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="gp">...</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">sum</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">11</span><span class="p">))</span>
<span class="go">55</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">sum</span><span class="p">([])</span>
<span class="go">0</span>
</pre></div>
</div>
<p>Don&#8217;t use this example&#8217;s definition of <a class="reference internal" href="../library/functions.html#sum" title="sum"><tt class="xref py py-func docutils literal"><span class="pre">sum()</span></tt></a>: since summing numbers is
such a common need, a built-in function <tt class="docutils literal"><span class="pre">sum(sequence)</span></tt> is already provided,
and works exactly like this.</p>
</div>
<div class="section" id="list-comprehensions">
<span id="tut-listcomps"></span><h3>5.1.4. List Comprehensions<a class="headerlink" href="#list-comprehensions" title="Permalink to this headline">¶</a></h3>
<p>List comprehensions provide a concise way to create lists.
Common applications are to make new lists where each element is the result of
some operations applied to each member of another sequence or iterable, or to
create a subsequence of those elements that satisfy a certain condition.</p>
<p>For example, assume we want to create a list of squares, like:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="n">squares</span> <span class="o">=</span> <span class="p">[]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">):</span>
<span class="gp">... </span>    <span class="n">squares</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">...</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">squares</span>
<span class="go">[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]</span>
</pre></div>
</div>
<p>We can obtain the same result with:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">squares</span> <span class="o">=</span> <span class="p">[</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">)]</span>
</pre></div>
</div>
<p>This is also equivalent to <tt class="docutils literal"><span class="pre">squares</span> <span class="pre">=</span> <span class="pre">map(lambda</span> <span class="pre">x:</span> <span class="pre">x**2,</span> <span class="pre">range(10))</span></tt>,
but it&#8217;s more concise and readable.</p>
<p>A list comprehension consists of brackets containing an expression followed
by a <a class="reference internal" href="../reference/compound_stmts.html#for"><tt class="xref std std-keyword docutils literal"><span class="pre">for</span></tt></a> clause, then zero or more <a class="reference internal" href="../reference/compound_stmts.html#for"><tt class="xref std std-keyword docutils literal"><span class="pre">for</span></tt></a> or <a class="reference internal" href="../reference/compound_stmts.html#if"><tt class="xref std std-keyword docutils literal"><span class="pre">if</span></tt></a>
clauses.  The result will be a new list resulting from evaluating the expression
in the context of the <a class="reference internal" href="../reference/compound_stmts.html#for"><tt class="xref std std-keyword docutils literal"><span class="pre">for</span></tt></a> and <a class="reference internal" href="../reference/compound_stmts.html#if"><tt class="xref std std-keyword docutils literal"><span class="pre">if</span></tt></a> clauses which follow it.
For example, this listcomp combines the elements of two lists if they are not
equal:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="p">[(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">]</span> <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">4</span><span class="p">]</span> <span class="k">if</span> <span class="n">x</span> <span class="o">!=</span> <span class="n">y</span><span class="p">]</span>
<span class="go">[(1, 3), (1, 4), (2, 3), (2, 1), (2, 4), (3, 1), (3, 4)]</span>
</pre></div>
</div>
<p>and it&#8217;s equivalent to:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="n">combs</span> <span class="o">=</span> <span class="p">[]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">]:</span>
<span class="gp">... </span>    <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">4</span><span class="p">]:</span>
<span class="gp">... </span>        <span class="k">if</span> <span class="n">x</span> <span class="o">!=</span> <span class="n">y</span><span class="p">:</span>
<span class="gp">... </span>            <span class="n">combs</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">))</span>
<span class="gp">...</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">combs</span>
<span class="go">[(1, 3), (1, 4), (2, 3), (2, 1), (2, 4), (3, 1), (3, 4)]</span>
</pre></div>
</div>
<p>Note how the order of the <a class="reference internal" href="../reference/compound_stmts.html#for"><tt class="xref std std-keyword docutils literal"><span class="pre">for</span></tt></a> and <a class="reference internal" href="../reference/compound_stmts.html#if"><tt class="xref std std-keyword docutils literal"><span class="pre">if</span></tt></a> statements is the
same in both these snippets.</p>
<p>If the expression is a tuple (e.g. the <tt class="docutils literal"><span class="pre">(x,</span> <span class="pre">y)</span></tt> in the previous example),
it must be parenthesized.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="n">vec</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="c"># create a new list with the values doubled</span>
<span class="gp">&gt;&gt;&gt; </span><span class="p">[</span><span class="n">x</span><span class="o">*</span><span class="mi">2</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">vec</span><span class="p">]</span>
<span class="go">[-8, -4, 0, 4, 8]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="c"># filter the list to exclude negative numbers</span>
<span class="gp">&gt;&gt;&gt; </span><span class="p">[</span><span class="n">x</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">vec</span> <span class="k">if</span> <span class="n">x</span> <span class="o">&gt;=</span> <span class="mi">0</span><span class="p">]</span>
<span class="go">[0, 2, 4]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="c"># apply a function to all the elements</span>
<span class="gp">&gt;&gt;&gt; </span><span class="p">[</span><span class="nb">abs</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">vec</span><span class="p">]</span>
<span class="go">[4, 2, 0, 2, 4]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="c"># call a method on each element</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">freshfruit</span> <span class="o">=</span> <span class="p">[</span><span class="s">&#39;  banana&#39;</span><span class="p">,</span> <span class="s">&#39;  loganberry &#39;</span><span class="p">,</span> <span class="s">&#39;passion fruit  &#39;</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="p">[</span><span class="n">weapon</span><span class="o">.</span><span class="n">strip</span><span class="p">()</span> <span class="k">for</span> <span class="n">weapon</span> <span class="ow">in</span> <span class="n">freshfruit</span><span class="p">]</span>
<span class="go">[&#39;banana&#39;, &#39;loganberry&#39;, &#39;passion fruit&#39;]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="c"># create a list of 2-tuples like (number, square)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="p">[(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">6</span><span class="p">)]</span>
<span class="go">[(0, 0), (1, 1), (2, 4), (3, 9), (4, 16), (5, 25)]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="c"># the tuple must be parenthesized, otherwise an error is raised</span>
<span class="gp">&gt;&gt;&gt; </span><span class="p">[</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">6</span><span class="p">)]</span>
  File <span class="nb">&quot;&lt;stdin&gt;&quot;</span>, line <span class="m">1</span>
    <span class="p">[</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">6</span><span class="p">)]</span>
               <span class="o">^</span>
<span class="nc">SyntaxError</span>: <span class="n-Identifier">invalid syntax</span>
<span class="gp">&gt;&gt;&gt; </span><span class="c"># flatten a list using a listcomp with two &#39;for&#39;</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">vec</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">],</span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span><span class="mi">8</span><span class="p">,</span><span class="mi">9</span><span class="p">]]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="p">[</span><span class="n">num</span> <span class="k">for</span> <span class="n">elem</span> <span class="ow">in</span> <span class="n">vec</span> <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">elem</span><span class="p">]</span>
<span class="go">[1, 2, 3, 4, 5, 6, 7, 8, 9]</span>
</pre></div>
</div>
<p>List comprehensions can contain complex expressions and nested functions:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">pi</span>
<span class="gp">&gt;&gt;&gt; </span><span class="p">[</span><span class="nb">str</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">pi</span><span class="p">,</span> <span class="n">i</span><span class="p">))</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">6</span><span class="p">)]</span>
<span class="go">[&#39;3.1&#39;, &#39;3.14&#39;, &#39;3.142&#39;, &#39;3.1416&#39;, &#39;3.14159&#39;]</span>
</pre></div>
</div>
<div class="section" id="nested-list-comprehensions">
<h4>5.1.4.1. Nested List Comprehensions<a class="headerlink" href="#nested-list-comprehensions" title="Permalink to this headline">¶</a></h4>
<p>The initial expression in a list comprehension can be any arbitrary expression,
including another list comprehension.</p>
<p>Consider the following example of a 3x4 matrix implemented as a list of
3 lists of length 4:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="n">matrix</span> <span class="o">=</span> <span class="p">[</span>
<span class="gp">... </span>    <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span>
<span class="gp">... </span>    <span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">],</span>
<span class="gp">... </span>    <span class="p">[</span><span class="mi">9</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">12</span><span class="p">],</span>
<span class="gp">... </span><span class="p">]</span>
</pre></div>
</div>
<p>The following list comprehension will transpose rows and columns:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="p">[[</span><span class="n">row</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">matrix</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">4</span><span class="p">)]</span>
<span class="go">[[1, 5, 9], [2, 6, 10], [3, 7, 11], [4, 8, 12]]</span>
</pre></div>
</div>
<p>As we saw in the previous section, the nested listcomp is evaluated in
the context of the <a class="reference internal" href="../reference/compound_stmts.html#for"><tt class="xref std std-keyword docutils literal"><span class="pre">for</span></tt></a> that follows it, so this example is
equivalent to:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="n">transposed</span> <span class="o">=</span> <span class="p">[]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">4</span><span class="p">):</span>
<span class="gp">... </span>    <span class="n">transposed</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="n">row</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">matrix</span><span class="p">])</span>
<span class="gp">...</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">transposed</span>
<span class="go">[[1, 5, 9], [2, 6, 10], [3, 7, 11], [4, 8, 12]]</span>
</pre></div>
</div>
<p>which, in turn, is the same as:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="n">transposed</span> <span class="o">=</span> <span class="p">[]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">4</span><span class="p">):</span>
<span class="gp">... </span>    <span class="c"># the following 3 lines implement the nested listcomp</span>
<span class="gp">... </span>    <span class="n">transposed_row</span> <span class="o">=</span> <span class="p">[]</span>
<span class="gp">... </span>    <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">matrix</span><span class="p">:</span>
<span class="gp">... </span>        <span class="n">transposed_row</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">row</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<span class="gp">... </span>    <span class="n">transposed</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">transposed_row</span><span class="p">)</span>
<span class="gp">...</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">transposed</span>
<span class="go">[[1, 5, 9], [2, 6, 10], [3, 7, 11], [4, 8, 12]]</span>
</pre></div>
</div>
<p>In the real world, you should prefer built-in functions to complex flow statements.
The <a class="reference internal" href="../library/functions.html#zip" title="zip"><tt class="xref py py-func docutils literal"><span class="pre">zip()</span></tt></a> function would do a great job for this use case:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="n">matrix</span><span class="p">)</span>
<span class="go">[(1, 5, 9), (2, 6, 10), (3, 7, 11), (4, 8, 12)]</span>
</pre></div>
</div>
<p>See <a class="reference internal" href="controlflow.html#tut-unpacking-arguments"><em>Unpacking Argument Lists</em></a> for details on the asterisk in this line.</p>
</div>
</div>
</div>
<div class="section" id="the-del-statement">
<span id="tut-del"></span><h2>5.2. The <a class="reference internal" href="../reference/simple_stmts.html#del"><tt class="xref std std-keyword docutils literal"><span class="pre">del</span></tt></a> statement<a class="headerlink" href="#the-del-statement" title="Permalink to this headline">¶</a></h2>
<p>There is a way to remove an item from a list given its index instead of its
value: the <a class="reference internal" href="../reference/simple_stmts.html#del"><tt class="xref std std-keyword docutils literal"><span class="pre">del</span></tt></a> statement.  This differs from the <tt class="xref py py-meth docutils literal"><span class="pre">pop()</span></tt> method
which returns a value.  The <a class="reference internal" href="../reference/simple_stmts.html#del"><tt class="xref std std-keyword docutils literal"><span class="pre">del</span></tt></a> statement can also be used to remove
slices from a list or clear the entire list (which we did earlier by assignment
of an empty list to the slice).  For example:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">66.25</span><span class="p">,</span> <span class="mi">333</span><span class="p">,</span> <span class="mi">333</span><span class="p">,</span> <span class="mf">1234.5</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="k">del</span> <span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span>
<span class="go">[1, 66.25, 333, 333, 1234.5]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="k">del</span> <span class="n">a</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">4</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span>
<span class="go">[1, 66.25, 1234.5]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="k">del</span> <span class="n">a</span><span class="p">[:]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span>
<span class="go">[]</span>
</pre></div>
</div>
<p><a class="reference internal" href="../reference/simple_stmts.html#del"><tt class="xref std std-keyword docutils literal"><span class="pre">del</span></tt></a> can also be used to delete entire variables:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="k">del</span> <span class="n">a</span>
</pre></div>
</div>
<p>Referencing the name <tt class="docutils literal"><span class="pre">a</span></tt> hereafter is an error (at least until another value
is assigned to it).  We&#8217;ll find other uses for <a class="reference internal" href="../reference/simple_stmts.html#del"><tt class="xref std std-keyword docutils literal"><span class="pre">del</span></tt></a> later.</p>
</div>
<div class="section" id="tuples-and-sequences">
<span id="tut-tuples"></span><h2>5.3. Tuples and Sequences<a class="headerlink" href="#tuples-and-sequences" title="Permalink to this headline">¶</a></h2>
<p>We saw that lists and strings have many common properties, such as indexing and
slicing operations.  They are two examples of <em>sequence</em> data types (see
<a class="reference internal" href="../library/stdtypes.html#typesseq"><em>Sequence Types &#8212; str, unicode, list, tuple, bytearray, buffer, xrange</em></a>).  Since Python is an evolving language, other sequence data
types may be added.  There is also another standard sequence data type: the
<em>tuple</em>.</p>
<p>A tuple consists of a number of values separated by commas, for instance:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="n">t</span> <span class="o">=</span> <span class="mi">12345</span><span class="p">,</span> <span class="mi">54321</span><span class="p">,</span> <span class="s">&#39;hello!&#39;</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">t</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="go">12345</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">t</span>
<span class="go">(12345, 54321, &#39;hello!&#39;)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="c"># Tuples may be nested:</span>
<span class="gp">... </span><span class="n">u</span> <span class="o">=</span> <span class="n">t</span><span class="p">,</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">u</span>
<span class="go">((12345, 54321, &#39;hello!&#39;), (1, 2, 3, 4, 5))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="c"># Tuples are immutable:</span>
<span class="gp">... </span><span class="n">t</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">88888</span>
<span class="gt">Traceback (most recent call last):</span>
  File <span class="nb">&quot;&lt;stdin&gt;&quot;</span>, line <span class="m">1</span>, in <span class="n-Identifier">&lt;module&gt;</span>
<span class="nc">TypeError</span>: <span class="n-Identifier">&#39;tuple&#39; object does not support item assignment</span>
<span class="gp">&gt;&gt;&gt; </span><span class="c"># but they can contain mutable objects:</span>
<span class="gp">... </span><span class="n">v</span> <span class="o">=</span> <span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">v</span>
<span class="go">([1, 2, 3], [3, 2, 1])</span>
</pre></div>
</div>
<p>As you see, on output tuples are always enclosed in parentheses, so that nested
tuples are interpreted correctly; they may be input with or without surrounding
parentheses, although often parentheses are necessary anyway (if the tuple is
part of a larger expression).  It is not possible to assign to the individual
items of a tuple, however it is possible to create tuples which contain mutable
objects, such as lists.</p>
<p>Though tuples may seem similar to lists, they are often used in different
situations and for different purposes.
Tuples are <a class="reference internal" href="../glossary.html#term-immutable"><em class="xref std std-term">immutable</em></a>, and usually contain an heterogeneous sequence of
elements that are accessed via unpacking (see later in this section) or indexing
(or even by attribute in the case of <a class="reference internal" href="../library/collections.html#collections.namedtuple" title="collections.namedtuple"><tt class="xref py py-func docutils literal"><span class="pre">namedtuples</span></tt></a>).
Lists are <a class="reference internal" href="../glossary.html#term-mutable"><em class="xref std std-term">mutable</em></a>, and their elements are usually homogeneous and are
accessed by iterating over the list.</p>
<p>A special problem is the construction of tuples containing 0 or 1 items: the
syntax has some extra quirks to accommodate these.  Empty tuples are constructed
by an empty pair of parentheses; a tuple with one item is constructed by
following a value with a comma (it is not sufficient to enclose a single value
in parentheses). Ugly, but effective.  For example:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="n">empty</span> <span class="o">=</span> <span class="p">()</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">singleton</span> <span class="o">=</span> <span class="s">&#39;hello&#39;</span><span class="p">,</span>    <span class="c"># &lt;-- note trailing comma</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">len</span><span class="p">(</span><span class="n">empty</span><span class="p">)</span>
<span class="go">0</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">len</span><span class="p">(</span><span class="n">singleton</span><span class="p">)</span>
<span class="go">1</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">singleton</span>
<span class="go">(&#39;hello&#39;,)</span>
</pre></div>
</div>
<p>The statement <tt class="docutils literal"><span class="pre">t</span> <span class="pre">=</span> <span class="pre">12345,</span> <span class="pre">54321,</span> <span class="pre">'hello!'</span></tt> is an example of <em>tuple packing</em>:
the values <tt class="docutils literal"><span class="pre">12345</span></tt>, <tt class="docutils literal"><span class="pre">54321</span></tt> and <tt class="docutils literal"><span class="pre">'hello!'</span></tt> are packed together in a tuple.
The reverse operation is also possible:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span> <span class="o">=</span> <span class="n">t</span>
</pre></div>
</div>
<p>This is called, appropriately enough, <em>sequence unpacking</em> and works for any
sequence on the right-hand side.  Sequence unpacking requires the list of
variables on the left to have the same number of elements as the length of the
sequence.  Note that multiple assignment is really just a combination of tuple
packing and sequence unpacking.</p>
</div>
<div class="section" id="sets">
<span id="tut-sets"></span><h2>5.4. Sets<a class="headerlink" href="#sets" title="Permalink to this headline">¶</a></h2>
<p>Python also includes a data type for <em>sets</em>.  A set is an unordered collection
with no duplicate elements.  Basic uses include membership testing and
eliminating duplicate entries.  Set objects also support mathematical operations
like union, intersection, difference, and symmetric difference.</p>
<p>Curly braces or the <a class="reference internal" href="../library/stdtypes.html#set" title="set"><tt class="xref py py-func docutils literal"><span class="pre">set()</span></tt></a> function can be used to create sets.  Note: to
create an empty set you have to use <tt class="docutils literal"><span class="pre">set()</span></tt>, not <tt class="docutils literal"><span class="pre">{}</span></tt>; the latter creates an
empty dictionary, a data structure that we discuss in the next section.</p>
<p>Here is a brief demonstration:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="n">basket</span> <span class="o">=</span> <span class="p">[</span><span class="s">&#39;apple&#39;</span><span class="p">,</span> <span class="s">&#39;orange&#39;</span><span class="p">,</span> <span class="s">&#39;apple&#39;</span><span class="p">,</span> <span class="s">&#39;pear&#39;</span><span class="p">,</span> <span class="s">&#39;orange&#39;</span><span class="p">,</span> <span class="s">&#39;banana&#39;</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">fruit</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">basket</span><span class="p">)</span>               <span class="c"># create a set without duplicates</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">fruit</span>
<span class="go">set([&#39;orange&#39;, &#39;pear&#39;, &#39;apple&#39;, &#39;banana&#39;])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="s">&#39;orange&#39;</span> <span class="ow">in</span> <span class="n">fruit</span>                 <span class="c"># fast membership testing</span>
<span class="go">True</span>
<span class="gp">&gt;&gt;&gt; </span><span class="s">&#39;crabgrass&#39;</span> <span class="ow">in</span> <span class="n">fruit</span>
<span class="go">False</span>

<span class="gp">&gt;&gt;&gt; </span><span class="c"># Demonstrate set operations on unique letters from two words</span>
<span class="gp">...</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="s">&#39;abracadabra&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">b</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="s">&#39;alacazam&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span>                                  <span class="c"># unique letters in a</span>
<span class="go">set([&#39;a&#39;, &#39;r&#39;, &#39;b&#39;, &#39;c&#39;, &#39;d&#39;])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">-</span> <span class="n">b</span>                              <span class="c"># letters in a but not in b</span>
<span class="go">set([&#39;r&#39;, &#39;d&#39;, &#39;b&#39;])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">|</span> <span class="n">b</span>                              <span class="c"># letters in either a or b</span>
<span class="go">set([&#39;a&#39;, &#39;c&#39;, &#39;r&#39;, &#39;d&#39;, &#39;b&#39;, &#39;m&#39;, &#39;z&#39;, &#39;l&#39;])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">&amp;</span> <span class="n">b</span>                              <span class="c"># letters in both a and b</span>
<span class="go">set([&#39;a&#39;, &#39;c&#39;])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">^</span> <span class="n">b</span>                              <span class="c"># letters in a or b but not both</span>
<span class="go">set([&#39;r&#39;, &#39;d&#39;, &#39;b&#39;, &#39;m&#39;, &#39;z&#39;, &#39;l&#39;])</span>
</pre></div>
</div>
<p>Similarly to <a class="reference internal" href="#tut-listcomps"><em>list comprehensions</em></a>, set comprehensions
are also supported:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="p">{</span><span class="n">x</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="s">&#39;abracadabra&#39;</span> <span class="k">if</span> <span class="n">x</span> <span class="ow">not</span> <span class="ow">in</span> <span class="s">&#39;abc&#39;</span><span class="p">}</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span>
<span class="go">set([&#39;r&#39;, &#39;d&#39;])</span>
</pre></div>
</div>
</div>
<div class="section" id="dictionaries">
<span id="tut-dictionaries"></span><h2>5.5. Dictionaries<a class="headerlink" href="#dictionaries" title="Permalink to this headline">¶</a></h2>
<p>Another useful data type built into Python is the <em>dictionary</em> (see
<a class="reference internal" href="../library/stdtypes.html#typesmapping"><em>Mapping Types &#8212; dict</em></a>). Dictionaries are sometimes found in other languages as
&#8220;associative memories&#8221; or &#8220;associative arrays&#8221;.  Unlike sequences, which are
indexed by a range of numbers, dictionaries are indexed by <em>keys</em>, which can be
any immutable type; strings and numbers can always be keys.  Tuples can be used
as keys if they contain only strings, numbers, or tuples; if a tuple contains
any mutable object either directly or indirectly, it cannot be used as a key.
You can&#8217;t use lists as keys, since lists can be modified in place using index
assignments, slice assignments, or methods like <tt class="xref py py-meth docutils literal"><span class="pre">append()</span></tt> and
<tt class="xref py py-meth docutils literal"><span class="pre">extend()</span></tt>.</p>
<p>It is best to think of a dictionary as an unordered set of <em>key: value</em> pairs,
with the requirement that the keys are unique (within one dictionary). A pair of
braces creates an empty dictionary: <tt class="docutils literal"><span class="pre">{}</span></tt>. Placing a comma-separated list of
key:value pairs within the braces adds initial key:value pairs to the
dictionary; this is also the way dictionaries are written on output.</p>
<p>The main operations on a dictionary are storing a value with some key and
extracting the value given the key.  It is also possible to delete a key:value
pair with <tt class="docutils literal"><span class="pre">del</span></tt>. If you store using a key that is already in use, the old
value associated with that key is forgotten.  It is an error to extract a value
using a non-existent key.</p>
<p>The <tt class="xref py py-meth docutils literal"><span class="pre">keys()</span></tt> method of a dictionary object returns a list of all the keys
used in the dictionary, in arbitrary order (if you want it sorted, just apply
the <a class="reference internal" href="../library/functions.html#sorted" title="sorted"><tt class="xref py py-func docutils literal"><span class="pre">sorted()</span></tt></a> function to it).  To check whether a single key is in the
dictionary, use the <a class="reference internal" href="../reference/expressions.html#in"><tt class="xref std std-keyword docutils literal"><span class="pre">in</span></tt></a> keyword.</p>
<p>Here is a small example using a dictionary:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="n">tel</span> <span class="o">=</span> <span class="p">{</span><span class="s">&#39;jack&#39;</span><span class="p">:</span> <span class="mi">4098</span><span class="p">,</span> <span class="s">&#39;sape&#39;</span><span class="p">:</span> <span class="mi">4139</span><span class="p">}</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">tel</span><span class="p">[</span><span class="s">&#39;guido&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="mi">4127</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">tel</span>
<span class="go">{&#39;sape&#39;: 4139, &#39;guido&#39;: 4127, &#39;jack&#39;: 4098}</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">tel</span><span class="p">[</span><span class="s">&#39;jack&#39;</span><span class="p">]</span>
<span class="go">4098</span>
<span class="gp">&gt;&gt;&gt; </span><span class="k">del</span> <span class="n">tel</span><span class="p">[</span><span class="s">&#39;sape&#39;</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">tel</span><span class="p">[</span><span class="s">&#39;irv&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="mi">4127</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">tel</span>
<span class="go">{&#39;guido&#39;: 4127, &#39;irv&#39;: 4127, &#39;jack&#39;: 4098}</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">tel</span><span class="o">.</span><span class="n">keys</span><span class="p">()</span>
<span class="go">[&#39;guido&#39;, &#39;irv&#39;, &#39;jack&#39;]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="s">&#39;guido&#39;</span> <span class="ow">in</span> <span class="n">tel</span>
<span class="go">True</span>
</pre></div>
</div>
<p>The <a class="reference internal" href="../library/stdtypes.html#dict" title="dict"><tt class="xref py py-func docutils literal"><span class="pre">dict()</span></tt></a> constructor builds dictionaries directly from sequences of
key-value pairs:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="nb">dict</span><span class="p">([(</span><span class="s">&#39;sape&#39;</span><span class="p">,</span> <span class="mi">4139</span><span class="p">),</span> <span class="p">(</span><span class="s">&#39;guido&#39;</span><span class="p">,</span> <span class="mi">4127</span><span class="p">),</span> <span class="p">(</span><span class="s">&#39;jack&#39;</span><span class="p">,</span> <span class="mi">4098</span><span class="p">)])</span>
<span class="go">{&#39;sape&#39;: 4139, &#39;jack&#39;: 4098, &#39;guido&#39;: 4127}</span>
</pre></div>
</div>
<p>In addition, dict comprehensions can be used to create dictionaries from
arbitrary key and value expressions:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="p">{</span><span class="n">x</span><span class="p">:</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">6</span><span class="p">)}</span>
<span class="go">{2: 4, 4: 16, 6: 36}</span>
</pre></div>
</div>
<p>When the keys are simple strings, it is sometimes easier to specify pairs using
keyword arguments:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="nb">dict</span><span class="p">(</span><span class="n">sape</span><span class="o">=</span><span class="mi">4139</span><span class="p">,</span> <span class="n">guido</span><span class="o">=</span><span class="mi">4127</span><span class="p">,</span> <span class="n">jack</span><span class="o">=</span><span class="mi">4098</span><span class="p">)</span>
<span class="go">{&#39;sape&#39;: 4139, &#39;jack&#39;: 4098, &#39;guido&#39;: 4127}</span>
</pre></div>
</div>
</div>
<div class="section" id="looping-techniques">
<span id="tut-loopidioms"></span><h2>5.6. Looping Techniques<a class="headerlink" href="#looping-techniques" title="Permalink to this headline">¶</a></h2>
<p>When looping through a sequence, the position index and corresponding value can
be retrieved at the same time using the <a class="reference internal" href="../library/functions.html#enumerate" title="enumerate"><tt class="xref py py-func docutils literal"><span class="pre">enumerate()</span></tt></a> function.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">v</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">([</span><span class="s">&#39;tic&#39;</span><span class="p">,</span> <span class="s">&#39;tac&#39;</span><span class="p">,</span> <span class="s">&#39;toe&#39;</span><span class="p">]):</span>
<span class="gp">... </span>    <span class="k">print</span> <span class="n">i</span><span class="p">,</span> <span class="n">v</span>
<span class="gp">...</span>
<span class="go">0 tic</span>
<span class="go">1 tac</span>
<span class="go">2 toe</span>
</pre></div>
</div>
<p>To loop over two or more sequences at the same time, the entries can be paired
with the <a class="reference internal" href="../library/functions.html#zip" title="zip"><tt class="xref py py-func docutils literal"><span class="pre">zip()</span></tt></a> function.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="n">questions</span> <span class="o">=</span> <span class="p">[</span><span class="s">&#39;name&#39;</span><span class="p">,</span> <span class="s">&#39;quest&#39;</span><span class="p">,</span> <span class="s">&#39;favorite color&#39;</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">answers</span> <span class="o">=</span> <span class="p">[</span><span class="s">&#39;lancelot&#39;</span><span class="p">,</span> <span class="s">&#39;the holy grail&#39;</span><span class="p">,</span> <span class="s">&#39;blue&#39;</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">q</span><span class="p">,</span> <span class="n">a</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">questions</span><span class="p">,</span> <span class="n">answers</span><span class="p">):</span>
<span class="gp">... </span>    <span class="k">print</span> <span class="s">&#39;What is your {0}?  It is {1}.&#39;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">q</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span>
<span class="gp">...</span>
<span class="go">What is your name?  It is lancelot.</span>
<span class="go">What is your quest?  It is the holy grail.</span>
<span class="go">What is your favorite color?  It is blue.</span>
</pre></div>
</div>
<p>To loop over a sequence in reverse, first specify the sequence in a forward
direction and then call the <a class="reference internal" href="../library/functions.html#reversed" title="reversed"><tt class="xref py py-func docutils literal"><span class="pre">reversed()</span></tt></a> function.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">reversed</span><span class="p">(</span><span class="nb">xrange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">10</span><span class="p">,</span><span class="mi">2</span><span class="p">)):</span>
<span class="gp">... </span>    <span class="k">print</span> <span class="n">i</span>
<span class="gp">...</span>
<span class="go">9</span>
<span class="go">7</span>
<span class="go">5</span>
<span class="go">3</span>
<span class="go">1</span>
</pre></div>
</div>
<p>To loop over a sequence in sorted order, use the <a class="reference internal" href="../library/functions.html#sorted" title="sorted"><tt class="xref py py-func docutils literal"><span class="pre">sorted()</span></tt></a> function which
returns a new sorted list while leaving the source unaltered.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="n">basket</span> <span class="o">=</span> <span class="p">[</span><span class="s">&#39;apple&#39;</span><span class="p">,</span> <span class="s">&#39;orange&#39;</span><span class="p">,</span> <span class="s">&#39;apple&#39;</span><span class="p">,</span> <span class="s">&#39;pear&#39;</span><span class="p">,</span> <span class="s">&#39;orange&#39;</span><span class="p">,</span> <span class="s">&#39;banana&#39;</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">basket</span><span class="p">)):</span>
<span class="gp">... </span>    <span class="k">print</span> <span class="n">f</span>
<span class="gp">...</span>
<span class="go">apple</span>
<span class="go">banana</span>
<span class="go">orange</span>
<span class="go">pear</span>
</pre></div>
</div>
<p>When looping through dictionaries, the key and corresponding value can be
retrieved at the same time using the <tt class="xref py py-meth docutils literal"><span class="pre">iteritems()</span></tt> method.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="n">knights</span> <span class="o">=</span> <span class="p">{</span><span class="s">&#39;gallahad&#39;</span><span class="p">:</span> <span class="s">&#39;the pure&#39;</span><span class="p">,</span> <span class="s">&#39;robin&#39;</span><span class="p">:</span> <span class="s">&#39;the brave&#39;</span><span class="p">}</span>
<span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">knights</span><span class="o">.</span><span class="n">iteritems</span><span class="p">():</span>
<span class="gp">... </span>    <span class="k">print</span> <span class="n">k</span><span class="p">,</span> <span class="n">v</span>
<span class="gp">...</span>
<span class="go">gallahad the pure</span>
<span class="go">robin the brave</span>
</pre></div>
</div>
<p>To change a sequence you are iterating over while inside the loop (for
example to duplicate certain items), it is recommended that you first make
a copy.  Looping over a sequence does not implicitly make a copy.  The slice
notation makes this especially convenient:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="n">words</span> <span class="o">=</span> <span class="p">[</span><span class="s">&#39;cat&#39;</span><span class="p">,</span> <span class="s">&#39;window&#39;</span><span class="p">,</span> <span class="s">&#39;defenestrate&#39;</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">w</span> <span class="ow">in</span> <span class="n">words</span><span class="p">[:]:</span>  <span class="c"># Loop over a slice copy of the entire list.</span>
<span class="gp">... </span>    <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">w</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">6</span><span class="p">:</span>
<span class="gp">... </span>        <span class="n">words</span><span class="o">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">w</span><span class="p">)</span>
<span class="gp">...</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">words</span>
<span class="go">[&#39;defenestrate&#39;, &#39;cat&#39;, &#39;window&#39;, &#39;defenestrate&#39;]</span>
</pre></div>
</div>
</div>
<div class="section" id="more-on-conditions">
<span id="tut-conditions"></span><h2>5.7. More on Conditions<a class="headerlink" href="#more-on-conditions" title="Permalink to this headline">¶</a></h2>
<p>The conditions used in <tt class="docutils literal"><span class="pre">while</span></tt> and <tt class="docutils literal"><span class="pre">if</span></tt> statements can contain any
operators, not just comparisons.</p>
<p>The comparison operators <tt class="docutils literal"><span class="pre">in</span></tt> and <tt class="docutils literal"><span class="pre">not</span> <span class="pre">in</span></tt> check whether a value occurs
(does not occur) in a sequence.  The operators <tt class="docutils literal"><span class="pre">is</span></tt> and <tt class="docutils literal"><span class="pre">is</span> <span class="pre">not</span></tt> compare
whether two objects are really the same object; this only matters for mutable
objects like lists.  All comparison operators have the same priority, which is
lower than that of all numerical operators.</p>
<p>Comparisons can be chained.  For example, <tt class="docutils literal"><span class="pre">a</span> <span class="pre">&lt;</span> <span class="pre">b</span> <span class="pre">==</span> <span class="pre">c</span></tt> tests whether <tt class="docutils literal"><span class="pre">a</span></tt> is
less than <tt class="docutils literal"><span class="pre">b</span></tt> and moreover <tt class="docutils literal"><span class="pre">b</span></tt> equals <tt class="docutils literal"><span class="pre">c</span></tt>.</p>
<p>Comparisons may be combined using the Boolean operators <tt class="docutils literal"><span class="pre">and</span></tt> and <tt class="docutils literal"><span class="pre">or</span></tt>, and
the outcome of a comparison (or of any other Boolean expression) may be negated
with <tt class="docutils literal"><span class="pre">not</span></tt>.  These have lower priorities than comparison operators; between
them, <tt class="docutils literal"><span class="pre">not</span></tt> has the highest priority and <tt class="docutils literal"><span class="pre">or</span></tt> the lowest, so that <tt class="docutils literal"><span class="pre">A</span> <span class="pre">and</span>
<span class="pre">not</span> <span class="pre">B</span> <span class="pre">or</span> <span class="pre">C</span></tt> is equivalent to <tt class="docutils literal"><span class="pre">(A</span> <span class="pre">and</span> <span class="pre">(not</span> <span class="pre">B))</span> <span class="pre">or</span> <span class="pre">C</span></tt>. As always, parentheses
can be used to express the desired composition.</p>
<p>The Boolean operators <tt class="docutils literal"><span class="pre">and</span></tt> and <tt class="docutils literal"><span class="pre">or</span></tt> are so-called <em>short-circuit</em>
operators: their arguments are evaluated from left to right, and evaluation
stops as soon as the outcome is determined.  For example, if <tt class="docutils literal"><span class="pre">A</span></tt> and <tt class="docutils literal"><span class="pre">C</span></tt> are
true but <tt class="docutils literal"><span class="pre">B</span></tt> is false, <tt class="docutils literal"><span class="pre">A</span> <span class="pre">and</span> <span class="pre">B</span> <span class="pre">and</span> <span class="pre">C</span></tt> does not evaluate the expression
<tt class="docutils literal"><span class="pre">C</span></tt>.  When used as a general value and not as a Boolean, the return value of a
short-circuit operator is the last evaluated argument.</p>
<p>It is possible to assign the result of a comparison or other Boolean expression
to a variable.  For example,</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="n">string1</span><span class="p">,</span> <span class="n">string2</span><span class="p">,</span> <span class="n">string3</span> <span class="o">=</span> <span class="s">&#39;&#39;</span><span class="p">,</span> <span class="s">&#39;Trondheim&#39;</span><span class="p">,</span> <span class="s">&#39;Hammer Dance&#39;</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">non_null</span> <span class="o">=</span> <span class="n">string1</span> <span class="ow">or</span> <span class="n">string2</span> <span class="ow">or</span> <span class="n">string3</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">non_null</span>
<span class="go">&#39;Trondheim&#39;</span>
</pre></div>
</div>
<p>Note that in Python, unlike C, assignment cannot occur inside expressions. C
programmers may grumble about this, but it avoids a common class of problems
encountered in C programs: typing <tt class="docutils literal"><span class="pre">=</span></tt> in an expression when <tt class="docutils literal"><span class="pre">==</span></tt> was
intended.</p>
</div>
<div class="section" id="comparing-sequences-and-other-types">
<span id="tut-comparing"></span><h2>5.8. Comparing Sequences and Other Types<a class="headerlink" href="#comparing-sequences-and-other-types" title="Permalink to this headline">¶</a></h2>
<p>Sequence objects may be compared to other objects with the same sequence type.
The comparison uses <em>lexicographical</em> ordering: first the first two items are
compared, and if they differ this determines the outcome of the comparison; if
they are equal, the next two items are compared, and so on, until either
sequence is exhausted. If two items to be compared are themselves sequences of
the same type, the lexicographical comparison is carried out recursively.  If
all items of two sequences compare equal, the sequences are considered equal.
If one sequence is an initial sub-sequence of the other, the shorter sequence is
the smaller (lesser) one.  Lexicographical ordering for strings uses the ASCII
ordering for individual characters.  Some examples of comparisons between
sequences of the same type:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>              <span class="o">&lt;</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span>              <span class="o">&lt;</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">]</span>
<span class="s">&#39;ABC&#39;</span> <span class="o">&lt;</span> <span class="s">&#39;C&#39;</span> <span class="o">&lt;</span> <span class="s">&#39;Pascal&#39;</span> <span class="o">&lt;</span> <span class="s">&#39;Python&#39;</span>
<span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>           <span class="o">&lt;</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
<span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>                 <span class="o">&lt;</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>             <span class="o">==</span> <span class="p">(</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">)</span>
<span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="s">&#39;aa&#39;</span><span class="p">,</span> <span class="s">&#39;ab&#39;</span><span class="p">))</span>   <span class="o">&lt;</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="s">&#39;abc&#39;</span><span class="p">,</span> <span class="s">&#39;a&#39;</span><span class="p">),</span> <span class="mi">4</span><span class="p">)</span>
</pre></div>
</div>
<p>Note that comparing objects of different types is legal.  The outcome is
deterministic but arbitrary: the types are ordered by their name. Thus, a list
is always smaller than a string, a string is always smaller than a tuple, etc.
<a class="footnote-reference" href="#id3" id="id2">[1]</a> Mixed numeric types are compared according to their numeric value, so 0
equals 0.0, etc.</p>
<p class="rubric">Footnotes</p>
<table class="docutils footnote" frame="void" id="id3" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id2">[1]</a></td><td>The rules for comparing objects of different types should not be relied upon;
they may change in a future version of the language.</td></tr>
</tbody>
</table>
</div>
</div>


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  <h3><a href="../contents.html">Table Of Contents</a></h3>
  <ul>
<li><a class="reference internal" href="#">5. Data Structures</a><ul>
<li><a class="reference internal" href="#more-on-lists">5.1. More on Lists</a><ul>
<li><a class="reference internal" href="#using-lists-as-stacks">5.1.1. Using Lists as Stacks</a></li>
<li><a class="reference internal" href="#using-lists-as-queues">5.1.2. Using Lists as Queues</a></li>
<li><a class="reference internal" href="#functional-programming-tools">5.1.3. Functional Programming Tools</a></li>
<li><a class="reference internal" href="#list-comprehensions">5.1.4. List Comprehensions</a><ul>
<li><a class="reference internal" href="#nested-list-comprehensions">5.1.4.1. Nested List Comprehensions</a></li>
</ul>
</li>
</ul>
</li>
<li><a class="reference internal" href="#the-del-statement">5.2. The <tt class="docutils literal"><span class="pre">del</span></tt> statement</a></li>
<li><a class="reference internal" href="#tuples-and-sequences">5.3. Tuples and Sequences</a></li>
<li><a class="reference internal" href="#sets">5.4. Sets</a></li>
<li><a class="reference internal" href="#dictionaries">5.5. Dictionaries</a></li>
<li><a class="reference internal" href="#looping-techniques">5.6. Looping Techniques</a></li>
<li><a class="reference internal" href="#more-on-conditions">5.7. More on Conditions</a></li>
<li><a class="reference internal" href="#comparing-sequences-and-other-types">5.8. Comparing Sequences and Other Types</a></li>
</ul>
</li>
</ul>

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